Surface Structures / Phyllotaxis / Alloys / Organic Structures2D and 3D lattice complexes with increased self-coordination numbers T i , i = 1 − 3, of nearest, second and third neighbors were derived for characteristic Wyckoff sets with zero or one parameters. Structure types of adsorbed atoms in 2D or elements A in 3D and A x B y compounds are approximated to the list of lattice complexes. Covalent bonding or electronic effects of atoms like lone electron pairs or Jahn-Teller distortion give rise to deviations from lattice complexes. Homogeneous structures A x B y with identical A-A or B-B self-coordination numbers T 1 , T 2 , T 3 of nearest, next-nearest and third neighbors are selected for different systems like magnetic ordering with A = ⊕ and B = spin direction or crystals of organic molecules with different orientations.